Definition:Minimum Value of Real Function/Absolute
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Definition
Let $f: \R \to \R$ be a real function.
Let $f$ be bounded below by an infimum $B$.
It may or may not be the case that $\exists x \in \R: \map f x = B$.
If such a value exists, it is called the minimum value of $f$ on $S$, and this minimum is attained at $x$.
Also known as
An absolute minimum is also known as a minimum value, or just a minimum if there is no need to distinguish it from a local minimum.
Also see
Sources
- 1977: K.G. Binmore: Mathematical Analysis: A Straightforward Approach ... (previous) ... (next): $\S 7.13$
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): absolute maximum or minimum
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): minimum (plural minima)
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): absolute maximum or minimum
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): minimum (plural minima)